The familiar use of the term to an authority figure helps to establish it in the mind of the reader. In the era before the hologram, this was the way that people visualized a three-dimension imaging system. You had to be able to walk around it to see all the details.

"If we don't show the Man from Mars in the stereo tanks pretty shortly, you'll have riots on your hands, Mr. Secretary."

If this was really three-dimensional, would you be able to walk behind a newscaster and see the back of his head? On the other hand, maybe it was really "stereo" vision, that is, an experience designed to be experienced from one direction - like a concert broadcast in stereo, with the illusion of depth and direction of sound.

Curmudgeon and contrarian Jubal Harshaw also refers to it as a "babble box", which is probably an inside joke for sf fans, who recall the babble machine from H.G. Wells' 1899 novel When the Sleeper Wakes. (Thanks to R. Philip Reynolds for that observation in a comment on another item.)

You might also want to see the entry for stereovision, from the same novel.

Heinlein probably derived the idea for this from the 3D tank from EE 'Doc' Smith's 1934 story Triplanetary.